edit mode grab tool doesn't work as expected
Your vertices and edges have been inadvertently set to be split automatically. Find the Options pulldown in the very top-right of the 3D View. Inside of it is the checkbox.

NOTE: If you don't see the Options pulldown at the top right of your screen, it may be that your Tool Settings bar has been disabled. To re-enable it, float your cursor just to the outer edge of any  one of the clickable buttons at the top of your 3D view (such as the buttons for View, Select, Add, etc.), but without your cursor actually touching those buttons. When your cursor changes from a cross to an arrow, right click, and you will get the option to turn on the Tool Settings. Then you will see the Options pulldown. From there you can turn off Split Edges &amp; Faces.